Question: Rewrite as a simplified fraction. ${3.\overline{82} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 382.8282...\\ 1x &= 3.8282...\end{align*}}$ Subtracting the two equations, we have: ${99x = 379}$ ${x = \dfrac{379}{99}} \text{or} {3 \dfrac{82}{99}}$